Theorem tpcomb 4701

Description: Swap 2nd and 3rd members of an unordered triple. (Contributed by NM, 22-May-2015.)

Assertion

Ref	Expression
tpcomb	⊢ {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}

Proof of Theorem tpcomb

Step	Hyp	Ref	Expression
1		tpcoma 4700	. 2 ⊢ {𝐵, 𝐶, 𝐴} = {𝐶, 𝐵, 𝐴}
2		tprot 4699	. 2 ⊢ {𝐴, 𝐵, 𝐶} = {𝐵, 𝐶, 𝐴}
3		tprot 4699	. 2 ⊢ {𝐴, 𝐶, 𝐵} = {𝐶, 𝐵, 𝐴}
4	1, 2, 3	3eqtr4i 2764	1 ⊢ {𝐴, 𝐵, 𝐶} = {𝐴, 𝐶, 𝐵}

Syntax hints:   = wceq 1541  {ctp 4577

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3or 1087  df-tru 1544  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-v 3438  df-un 3902  df-sn 4574  df-pr 4576  df-tp 4578

This theorem is referenced by:  f13dfv  7208  frgr3v  30255  tpssad  32519  signswch  34574  signstfvcl  34586  dvh4dimN  41494